1. The hypercentral Constituent Quark Model
Longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model
The hypercentral Constituent Quark Model
Results for the longitudinal and transverse helicity amplitudes
High Q2 behaviour
Meson cloud and/or quark-antiquark pair effects
Conclusions
M. Giannini N-N* transition from factors Jlab, october 2008

2. The hypercentral Constituent Quark Model
hCQM
The description of the spectrum is the first task of a model builder:
it serves to determine a quark interaction to be used for the
description of other physical quantitites
LQCD (De Rújula, Georgi, Glashow, 1975)
the quark interaction contains
a long range spin-independent confinement
SU(6) invariant
a short range spin dependent term
SU(6) violation
SU(6) configurations

3. Non strange baryons states with 4 and 3 stars in the PDG rating

4. x =
 
hyperradius

5. V = - b/r + c r Quark-antiquark lattice potential
G.S. Bali Phys. Rep. 343, 1 (2001)
V = - b/r + c r

7. V(x) = - t/x + a x
P = P = P = -1
Non strange baryons states with 4 and 3 stars in the PDG rating

8. hCQM & Electromagnetic properties
Photocouplings
Helicity amplitudes (transition f.f.)
Elastic form factors of the nucleon
Structure functions
Fixed parameters predictions

9. A1/2 = < N* Jz = 1/2 | HTem | N Jz = -1/2 > * §
HELICITY AMPLITUDES
Definition
A1/2 = < N* Jz = 1/2 | HTem | N Jz = -1/2 > * §
A3/2 = < N* Jz = 3/2 | HTem | N Jz = 1/2 > * §
S1/2 = < N* Jz = 1/2 | HLem | N Jz = 1/2 > * 
N, N* nucleon and resonance as 3q states
HTem Hlem model transition operator
 overall sign -> problem
§ results for the negative parity resonances: M. Aiello et al. J. Phys. G24, 753 (1998)

10. Photoproduction amplitude π N*
Theory:
states are defined up to a phase factor
N -> N ei N* -> N* ei N N
<N*|H|N>
<N*|H|N>
the overall sign is left unchanged  π N*
Phenomenology:
Overall sign relative to Born amplitude N N
A1/2 A3/2 S1/2
In order to extract the helicity amplitudes the sign of the strong vertex is used
Need for : a definite way of extracting the photon vertex
a general consensus

11. 10-3 GeV-1/2
for a comparison with data: M. Aiello et al., Phys. Lett. B387, 215 (1996)

13. m = 3/2
m = 1/2
Green curves H.O.
Blue curves hCQM

24. please note the calculated proton radius is about 0.5 fm
(value previously obtained by fitting the helicity amplitudes)
the medium Q2 behaviour is fairly well reproduced
there is lack of strength at low Q2 (outer region) in the e.m. transitions
specially for the A 3/2 amplitudes
emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud
“On the other hand, the confinement radius of ≈ 0.5 fm, which is currently used in order to give
reasonable results for the photocouplings, is substantially lower than the proton charge radius
and this seems to indicate that other mechanisms, such as pair production and sea quark contributions
may be relevant.”
M. Aiello, M. Ferraris, M.M.G, M. Pizzo, E. Santopinto, Phys.Lett.B387, 215 (1996).

25. Bare vs dressed quantities
QM calculations
the aim is the description of observables not a fit
(dressed quantities )
with success: spectrum, magnetic moments, …
the separation between bare and dressed quantities is meaningful within a definite theoretical approach
CQ have a mass, some dressing is implicitly taken into account
in fact CQs are effective degrees of freedom
something similar may occur in the spectrum
e.g. the consistent inclusion of quark loops effects in the meson description does not alter the form of the qqbar potential but renormalizes the string constant (Geiger-Isgur)
a consistent and systematic CQM approach may be helpful in order to put in evidence explicit dressing effects

26. Mainz-Dubna-Taiwan MAID -> 2007 Sato & Lee ………
Various approaches with mesons and baryons af effective degrees of freedom
Mainz-Dubna-Taiwan MAID -> 2007
Sato & Lee
………
e.g. MZ dynamical model
a systematic description (fit with free parameters) is obtained
with very good results

29. t v t t Explicit evaluation of the meson cloud contribution to
the excitation of the nucleon resonances (Mainz Group and coworkers) = + ~
t R R
v B ~
t
t R

30. GE-MZ coll., EPJA 2004 (Trieste 2003)

31. GE-MZ coll., EPJA 2004 (Trieste 2003)

32. GE-MZ coll., EPJA 2004 (Trieste 2003)

33. How to introduce dressing
hadronic approach: mesons and baryons (nucleon + resonances)
(equations for amplitudes, coupled channel calculations, lagrangians, …..
hybrid models
at the quark level
inclusion of higher Fock components in the baryon state
unquenching the quark model
Geiger-Isgur
Capstick, BRAG 2007
Santopinto-Bijker, Nstar2007

34. hep-ph/

35. High Q^2 behaviour Helicity ratio | A1/2 |2 – | A3/2 | 2
_____________________
| A1/2 |2 + | A3/2 | 2
goes to 1 for increasing Q2
(helicity conservation, Carlson 1986)

36. D hCQM predictions
Q^2 GeV^2

37. F hCQM predictions
Q^2 GeV^2

38. D hCQM predictions
Q^2 GeV^2

39. Helicity ratio Structure effects ? proton neutron P33 ≈ -0.5 D13 ok
proton
neutron
P33
≈ -0.5
D13 ok
F15
≈ 0.7
D13*
0.96
D33
D15
1/3
≈ 0.32
F35
-0.82
F37
-0.32
P13
Structure
effects ?

40. Phenomenological problems
Conclusions
Phenomenological problems
Sign of helicity amplitudes
PDG values (often average of quite different sets)
Need for more data
A comparison of systematic CQM results and data
understanding where meson cloud or (better) q-qbar effects are important (transition and elastic ff, structure functions,…..)
a good basis for including consistently these effects provided by (h)CQM

41. Conclusions (cont.) Theoretical problems
Relativity (probably not important for helicity amplitudes)
[relativistic hCQM -> elastic ff (PR C 2007)]
Consistent inclusion of quark-antiquark pair creation effects
Contributions from higher shells
Consequences of the inclusion of quark-antiquark pair creation effects:
Non zero width of resonances
Consistent evaluation of strong and e.m. vertices
Direct calculation of scattering electroproduction
……….
A substantial improvement in CQM calculations!